[SPARK-50023][PYTHON][CONNECT] API compatibility check for Functions

### What changes were proposed in this pull request?

This PR proposes to add API compatibility check for Spark SQL Functions

### Why are the changes needed?

To guarantee of the same behavior between Spark Classic and Spark Connect

### Does this PR introduce _any_ user-facing change?

No

### How was this patch tested?

Added UTs

### Was this patch authored or co-authored using generative AI tooling?

No

Closes apache#48536 from itholic/SPARK-50023.

Authored-by: Haejoon Lee <haejoon.lee@databricks.com>
Signed-off-by: Hyukjin Kwon <gurwls223@apache.org>

python/pyspark/sql/connect/functions/builtin.py

@@ -1498,7 +1498,7 @@ def lead(col: "ColumnOrName", offset: int = 1, default: Optional[Any] = None) ->
 lead.__doc__ = pysparkfuncs.lead.__doc__
 
 
-def nth_value(col: "ColumnOrName", offset: int, ignoreNulls: Optional[bool] = None) -> Column:
+def nth_value(col: "ColumnOrName", offset: int, ignoreNulls: Optional[bool] = False) -> Column:
     if ignoreNulls is None:
         return _invoke_function("nth_value", _to_col(col), lit(offset))
     else:
@@ -2236,7 +2236,7 @@ def size(col: "ColumnOrName") -> Column:
 
 
 def slice(
-    col: "ColumnOrName", start: Union["ColumnOrName", int], length: Union["ColumnOrName", int]
+    x: "ColumnOrName", start: Union["ColumnOrName", int], length: Union["ColumnOrName", int]
 ) -> Column:
     start = _enum_to_value(start)
     if isinstance(start, (Column, str)):
@@ -2260,7 +2260,7 @@ def slice(
             messageParameters={"arg_name": "length", "arg_type": type(length).__name__},
         )
 
-    return _invoke_function_over_columns("slice", col, _start, _length)
+    return _invoke_function_over_columns("slice", x, _start, _length)
 
 
 slice.__doc__ = pysparkfuncs.slice.__doc__
@@ -4195,6 +4195,7 @@ def unwrap_udt(col: "ColumnOrName") -> Column:
 def udf(
     f: Optional[Union[Callable[..., Any], "DataTypeOrString"]] = None,
     returnType: "DataTypeOrString" = StringType(),
+    *,
     useArrow: Optional[bool] = None,
 ) -> Union["UserDefinedFunctionLike", Callable[[Callable[..., Any]], "UserDefinedFunctionLike"]]:
     if f is None or isinstance(f, (str, DataType)):

python/pyspark/sql/functions/builtin.py

@@ -41,7 +41,7 @@
 
 from pyspark.errors import PySparkTypeError, PySparkValueError
 from pyspark.sql.column import Column
-from pyspark.sql.dataframe import DataFrame
+from pyspark.sql.dataframe import DataFrame as ParentDataFrame
 from pyspark.sql.types import ArrayType, DataType, StringType, StructType, _from_numpy_type
 
 # Keep UserDefinedFunction import for backwards compatible import; moved in SPARK-22409
@@ -5590,7 +5590,7 @@ def approx_count_distinct(col: "ColumnOrName", rsd: Optional[float] = None) -> C
 
 
 @_try_remote_functions
-def broadcast(df: DataFrame) -> DataFrame:
+def broadcast(df: "ParentDataFrame") -> "ParentDataFrame":
     """
     Marks a DataFrame as small enough for use in broadcast joins.
 
@@ -5621,7 +5621,7 @@ def broadcast(df: DataFrame) -> DataFrame:
     from py4j.java_gateway import JVMView
 
     sc = _get_active_spark_context()
-    return DataFrame(cast(JVMView, sc._jvm).functions.broadcast(df._jdf), df.sparkSession)
+    return ParentDataFrame(cast(JVMView, sc._jvm).functions.broadcast(df._jdf), df.sparkSession)
 
 
 @_try_remote_functions
@@ -9678,7 +9678,7 @@ def from_utc_timestamp(timestamp: "ColumnOrName", tz: Union[Column, str]) -> Col
 
 
 @_try_remote_functions
-def to_utc_timestamp(timestamp: "ColumnOrName", tz: "ColumnOrName") -> Column:
+def to_utc_timestamp(timestamp: "ColumnOrName", tz: Union[Column, str]) -> Column:
     """
     This is a common function for databases supporting TIMESTAMP WITHOUT TIMEZONE. This function
     takes a timestamp which is timezone-agnostic, and interprets it as a timestamp in the given

python/pyspark/sql/tests/test_connect_compatibility.py

@@ -30,6 +30,7 @@
 from pyspark.sql.readwriter import DataFrameWriterV2 as ClassicDataFrameWriterV2
 from pyspark.sql.window import Window as ClassicWindow
 from pyspark.sql.window import WindowSpec as ClassicWindowSpec
+import pyspark.sql.functions as ClassicFunctions
 
 if should_test_connect:
     from pyspark.sql.connect.dataframe import DataFrame as ConnectDataFrame
@@ -41,6 +42,7 @@
     from pyspark.sql.connect.readwriter import DataFrameWriterV2 as ConnectDataFrameWriterV2
     from pyspark.sql.connect.window import Window as ConnectWindow
     from pyspark.sql.connect.window import WindowSpec as ConnectWindowSpec
+    import pyspark.sql.connect.functions as ConnectFunctions
 
 
 class ConnectCompatibilityTestsMixin:
@@ -339,6 +341,22 @@ def test_window_spec_compatibility(self):
             expected_missing_classic_methods,
         )
 
+    def test_functions_compatibility(self):
+        """Test Functions compatibility between classic and connect."""
+        expected_missing_connect_properties = set()
+        expected_missing_classic_properties = set()
+        expected_missing_connect_methods = set()
+        expected_missing_classic_methods = {"check_dependencies"}
+        self.check_compatibility(
+            ClassicFunctions,
+            ConnectFunctions,
+            "Functions",
+            expected_missing_connect_properties,
+            expected_missing_classic_properties,
+            expected_missing_connect_methods,
+            expected_missing_classic_methods,
+        )
+
 
 @unittest.skipIf(not should_test_connect, connect_requirement_message)
 class ConnectCompatibilityTests(ConnectCompatibilityTestsMixin, ReusedSQLTestCase):